Investors wiped nearly 40 percent off the value of Tile Shop Holdings Inc., a Plymouth-based retailer of specialty tiles, after a short seller on Thursday accused it of overstating profits. The stock drop continued Friday.

In a report posted online shortly after the market opened, Gotham City Research said Tile Shop relies on a cozy relationship with its largest supplier to lower the cost it pays for tiles and inflate its profit margins.

In a response issued at midafternoon, Tile Shop announced it had suspended purchases with the supplier and said the relationship, which Gotham City said involved Tile Shop’s top executive and a relative, would be investigated.

“The company adamantly denies these allegations and believes that the financial statements are properly stated and its business practices are appropriate,” Tile Shop said in the statement.

It also reaffirmed the full-year sales guidance issued two weeks ago of a range of $227 million to $237 million, up from its 2012 revenue of $182.7 million.

Shares in Tile Shop fell $8.27, or 39 percent, to $12.95 by the time regulators halted trading in them with about an hour left to go in the regular trading day.

On Friday, Tile Shop shares see-sawed. They went down another 20 percent in the first 30 minutes of trading but recovered through the day as sell-side analysts issued reports countering some of the claims by Gotham City Research. They finished up nearly 12 percent at $14.50. For the week, Tile Shop shares were down 31 percent.

Roughly $400 million of the company’s $1 billion market capitalization evaporated during a frenzy in which 19.5 million shares traded hands. Tile Shop’s average daily trading volume was about 400,000 shares before Thursday.

Gotham City Research is one of a relatively small group of investment firms that make waves in financial markets by uncovering improprieties, buying short positions that make money when a stock’s price declines, then revealing the wrongdoing and making a profit. In its report on Tile Shop, Gotham City Research said it expected to make money from a decline in the company’s share price.

Tile Shop, which operates 82 stores in 27 states, became a public company in August 2012 through a reverse merger with a company called JWC Acquisition Corp. that was associated with a Waltham, Mass., private equity firm. Tile Shop completed a secondary stock offering last December.

The company’s shares rose from about $17 at the start of the year to around $30 during the summer. But they have been volatile all year and fell about 19 percent on the day last month when its third-quarter earnings missed expectations.

Gotham City Research said Tile Shop’s largest supplier is a Chinese firm controlled by the brother-in-law of Tile Shop CEO Robert Rucker. It said the brother-in-law is also a Tile Shop employee and his name appears on invoices of orders by Tile Shop to the Chinese firm, called Beijing Pingxiu.

Gotham City noted that Tile Shop had not disclosed the supplier, which it found by examining government trade data, to investors and speculated that the relationship may be contributing to a rise in the company’s inventories, which have grown faster than sales.

In its statement, Tile Shop did not directly address the allegation that Beijing Pingxiu is connected to Rucker’s brother-in-law.

“The company has been made aware of changes of the ownership of Beijing Pingxiu which were not previously disclosed to the company,’’ the statement said. ‘‘As a result of this disclosure, the company has suspended its relationship with this entity.”

Tile Shop added that it believes “any issues associated with the ownership of Beijing Pingxiu, or the utilization of other export trading companies, have had no material impact on the economics of inventory purchases.”

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